BUILT-IN MATHEMATICA SYMBOL

# LegendreQ

LegendreQ[n, z]
gives the Legendre function of the second kind .

LegendreQ[n, m, z]
gives the associated Legendre function of the second kind .

## DetailsDetails

• Mathematical function, suitable for both symbolic and numerical manipulation.
• For integers n and m, explicit formulas are generated.
• The Legendre functions satisfy the differential equation .
• LegendreQ[n, m, a, z] gives Legendre functions of type a. The default is type 1.
• LegendreQ of types 1, 2, and 3 are defined in terms of LegendreP of these types, and have the same branch cut structure.
• For certain special arguments, LegendreQ automatically evaluates to exact values.
• LegendreQ can be evaluated to arbitrary numerical precision.
• LegendreQ automatically threads over lists.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Compute the 5 Legendre function of the second kind:

 Out[1]=

Plot:

 Out[1]=

## TutorialsTutorials

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